Aristotle’s thoughts on Zeno’s Arrow Argument as represented in Chapter 9 of Aristotle’s Physics: A Guided Study can be understood in such a way that it might not be “next door to madness”.  In this chapter, Aristotle interprets Zeno’s argument of the Flying Arrow as “missing the mark”.  There are four premises for this argument, and in Aristotle’s opinion, premise three can be rejected. He does not believe that time is composed of indivisible nows, which he proves with laws of science. However, by evaluating the falsity of premise three, you will find that premises one and two are also false.  Almost all opinions can be argued, however, and by evaluating the philosophy of both men, many points can be reached about the validity and soundness of the argument.  Though, by finding the premises false, the argument is not sound, and therefore, Zeno’s argument leaves much to be said.

Deciphering from what we know of the argument by what Aristotle tells us in Chapter 9, the premises are sketched out:

1.  Everything is at rest when at a place equal to it;

2.  The Flying arrow is at rest when at a place equal to it;

3.  Time is composed of indivisible nows (instants).

4.  Everything that changes place is doing so in the now.

5.  Conclusion:  The flying arrow doesn’t move.

According to Zeno, time is composed of many indivisible nows, or instants.  Aristotle disagrees, stating in line 210 that no magnitude, including time, is composed of indivisible nows.  Exactly how long is an instant?  Is time finite?  As you start dividing time, the smaller you get, the less movement occurs.  But even when you do divide it smaller and smaller, is there not at least some small amount of movement occurring?  When will time get so small that movement does not occur?  This is Aristotle’s reasoning:  that time will never get to a “smallest” point, as length will never have a “smallest” division.  Therefore, he is rejecting the third premise, stating that time is not composed of indivisible segments.

How to Summarize

Zeno, however, feels that time can be divided into a “smallest” part.  After all, in physics, you can determine an object’s instantaneous velocity or acceleration at a specific point in its journey, at a specific time.  Wouldn’t this make time indivisible?

Velocity and acceleration are given to mean motion, which means the object is moving at this specific point in time.  Therefore, according to Aristotle, this paradox would not be so if it were not taken that time were composed of nows.

By rejecting this premise, and reevaluating the argument, you will read that premise one and two do not match anymore.  When you find that nothing is ever at rest because time is never standing still, then the Flying Arrow is never at rest.  This means that premises one and two are not true either, and this further complicates Zeno’s argument.

The reasoning from his standpoint makes sense, but by rejecting one premise using Aristotle’s rationalizing, we have now rejected two more.  Zeno’s argument has fallen apart.  The arrow is moving, and by following plain rules of science, we have found this to be true.

Zeno’s argument, as outlined in Aristotle’s studies, is perfectly valid.  He states that everything is at rest when at a place equal to it, which qualifies the arrow as a part of everything.  Therefore, the arrow would be at rest when at a place equal to it.  If the arrow is flying, then it is changing place, and everything that changes place is doing so in the now, so the arrow is changing place in the now.  If you use Zeno’s reasoning that time is composed of indivisible nows, you find that premise three is a true statement.  But considering we have found, according to the laws of physics, Aristotle’s views are correct, then the premise is false, and the argument is not sound.  We have gone over why Zeno’s reasoning about indivisible time segments is inaccurate, hence this will be the case.

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According to Aristotle, Zeno’s theories “go beyond perception and pay no attention to it, on the grounds that one is obliged to follow where the argument leads…”, and because Zeno seems to hold these opinions, Aristotle finds him “next door to madness.”  It seems to be that one is tempted to follow the argument, because without consulting the laws that hold true for motion and time, the argument will seem to be logical.  At this point in evaluating his argument, you must think into exactly what Zeno is stating and the opinions he is holding.  Certainly this is what Aristotle did, and what seems to be the correct idea, for he has found the faults in Zeno’s argument.

According to these points, both Zeno and Aristotle had the right ideas when formulating their arguments.  Zeno seemed to be neglecting many laws of science, and although Aristotle corrected him on many of these points, he did not seem to prove him “next door to madness”, as he states in Gen/Corr 325a12-17.  These seem to be points that Zeno had very different opinions on, and even though they may be wrong, they do not seem to be so inappropriate when you see where his argument leads, and where he wished it to go.  He had another way of interpreting what he saw. Zeno had a valid argument, we would have to agree, but the soundness did “miss the mark” by just a bit.  But this only rings true if you are obliged to “follow where the argument leads”.

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